Digital filter

ABSTRACT

A first stage of a digital filter receives input data to be filtered, the first stage of a digital filter operating at a first clock; a second stage of the digital filter outputs filtered output data, the second stage of the digital filter operating on a second clock, wherein a ratio of a frequency of the first clock and a frequency of the second clock is a fractional number, and a frequency of the second clock is higher than a frequency of the first clock; the first stage receives an indication of a ratio of the first clock and the second clock; and the first stage receives an indication of a time offset between (1) a clock pulse of the second clock, which occurs between a first clock pulse and a second clock pulse of the first clock, and (2) the first clock pulse of the first clock.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of co-pending U.S. patentapplication Ser. No. 12/201,465, filed Aug. 29, 2008, entitled “DigitalFilter,” hereby incorporated by reference as to its entirety.

BACKGROUND OF THE INVENTION

Digital circuits may comprise digital filters to convert input data of afirst frequency clock to output data of a second frequency clock. Forthe case of an interpolation filter the input data has a lower frequencyclock than the output data, while in a decimation filter the input datahas a higher frequency clock than its output data. Digital filters thusmay comprise multiple stages operating at different frequency clocks.

SUMMARY

Various aspects are described herein. For example, some aspects aredirected to methods and apparatuses in which a first stage of a digitalfilter receives input data to be filtered, the first stage of a digitalfilter operating at a first clock; a second stage of the digital filteroutputs filtered output data, the second stage of the digital filteroperating on a second clock, wherein a ratio of a frequency of the firstclock and a frequency of the second clock is a fractional number, and afrequency of the second clock is higher than a frequency of the firstclock; the first stage receives an indication of a ratio of the firstclock and the second clock; and the first stage receives an indicationof a time offset between (1) a clock pulse of the second clock, whichoccurs between a first clock pulse and a second clock pulse of the firstclock, and (2) the first clock pulse of the first clock.

These and other aspects will be described herein in the followingDetailed Description of Illustrative Embodiments.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

Various aspects as described herein are made more evident by way ofexample in the following detailed description of illustrativeembodiments when read in conjunction with the attached figures.

FIG. 1 shows an illustrative timing diagram 100.

FIG. 2 schematically illustrates a digital filter 200 as an exemplaryembodiment.

FIG. 3 schematically illustrates a digital filter 300 as an exemplaryembodiment.

FIG. 4 shows an illustrative pulse response 400.

FIG. 5 schematically illustrates a digital filter 500 as an exemplaryembodiment.

FIG. 6 schematically illustrates a digital filter 600 as an exemplaryembodiment.

FIG. 7 shows an illustrative pulse response 700.

FIG. 8 schematically illustrates a digital filter 800 as an exemplaryembodiment.

FIG. 9 schematically illustrates a digital filter 900 as an exemplaryembodiment.

FIG. 10 schematically illustrates a digital filter 1000 as an exemplaryembodiment.

FIG. 11 schematically illustrates a digital filter 1100 as an exemplaryembodiment.

FIG. 12 schematically illustrates a digital filter 1200 as an exemplaryembodiment.

FIG. 13 schematically illustrates a digital filter 1300 as an exemplaryembodiment.

FIG. 14 schematically illustrates a diagram 1400 illustrating anoperating mode of the digital filter 1300.

FIG. 15 schematically illustrates a digital device 1500 as an exemplaryembodiment.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

In the following one or more aspects and embodiments are described withreference to the drawings, wherein like reference numerals are generallyutilized to refer to like elements throughout. In the followingdescription, for purposes of explanation, numerous specific details areset forth in order to provide a thorough understanding. It may beevident, however, to one skilled in the art that one or more aspects asdescribed herein may be practiced with a lesser degree of these specificdetails. In other instances, known structures and devices are shown inblock diagram form in order to facilitate describing the one or moreaspects. The following description is not to be taken in a limitingsense, and rather should be taken in an illustrative sense.

In addition, while a particular feature or aspect of an embodiment maybe disclosed with respect to only one of several implementations, suchfeature or aspect may be combined with one or more other features oraspects of the other implementations as may be desired and advantageousfor any given or particular application. Furthermore, to the extent thatthe terms “include”, “have”, “with”, or other variants thereof are usedin either the disclosure or the claims, such terms are intended to beinclusive in the same manner as the term “comprise”. The terms “coupled”and “connected”, along with derivatives may be used. It should beunderstood that these terms may be used to indicate that two elementsco-operate or interact with each other regardless of whether they are indirect or indirect physical, electrical, or other type of communicativecontact, or they are not in direct contact with each other. Also, theterm “exemplary” or “illustrative” refers to merely an example, ratherthan necessarily the best or optimal.

FIG. 1 shows an illustrative timing diagram 100 based on a low frequencyclock and a high frequency clock, both starting at a time t₀. The terms“low” and “high” frequency as used herein are relative terms and do notimply any absolute frequency ranges. The timing diagram 100 shows threeclock pulses of the low frequency clock (cf. high peaks at timest_(1,1), t_(1,2) and t_(1,3)) and sixteen clock pulses of the highfrequency clock (cf. low peaks such as at time t₁). Since frequencyratios of the high frequency clock and the low frequency clockcorrespond to a fractional number (e.g. 16/3 or 3/16), the clock pulsesof the high frequency clock do not coincide with the clock pulses of thelow frequency clock at the times t_(1,1) and t_(1,2). The first time ofcoincidence between the two frequency clocks is given at the timet_(1,3).

During a first time interval between the times t₀ and t_(1,1) five clockpulses of the high frequency clock occur. Similarly, five clock pulsesof the high frequency clock occur during a second time interval betweenthe times t_(1,1) and t_(1,2). Here, the first clock pulse of the highfrequency clock in the second time interval (cf. time t_(h,1)) does notcoincide with the first clock pulse of the low frequency clock at thetime t_(1,1). Instead, the clock pulse of the high frequency clock atthe time t_(h,1) is arranged ⅔ (in units of the high frequency clock) tothe right of the time t_(1,1). A parameter μ_(O,1) denotes acorresponding value of the time offset.

A third time interval is given between the times t_(1,2) and t_(1,3).Six clock pulses of the high frequency clock occur in this third timeinterval, wherein the clock pulses of the low frequency clock and thehigh frequency clock coincide at the time t_(1,3). The first clock pulseof the high frequency clock in the third time interval (cf. timet_(h,2)) is arranged ⅓ (in units of the high frequency clock) to theright of the time t_(1,2). A corresponding value of the time offset isdenoted by a parameter μ_(O,2).

It is understood that further time intervals may succeed the describedthree time intervals. Such further time intervals may be obtained bysimply repeating the first three time intervals. For example, a fourthtime interval would then correspond to the first time interval, a fifthtime interval would correspond to the second time interval and a sixthtime interval would correspond to the third time interval.

FIG. 2 schematically illustrates a digital filter 200 as an exemplaryembodiment. For example, the digital filter 200 may be a Finite ImpulseResponse (FIR) filter as it may be used in digital signal processing.The digital filter 200 includes a first stage 1 operating at a lowfrequency clock and a second stage 2 operating at a high frequencyclock, wherein a ratio μ_(I) of the low frequency clock and the highfrequency clock may be a fractional number. Referring to FIG. 1, theratio μ_(I) may have a value of, for instance, 3/16 or 16/3.

The first stage 1 includes a first input 3 configured to receive inputdata to be filtered by the digital filter 200. For example, the inputdata may be represented by a bit sequence clocked with the low frequencyclock. A second input 4 of the digital filter 200 receives a signalrepresenting the ratio μ_(I) of the low frequency clock and the highfrequency clock, and a third input 5 receives a signal representing atime offset μ_(O) between a clock pulse of the high frequency clock,which occurs between a first clock pulse and a second clock pulse of thelow frequency clock, and the first clock pulse of the low frequencyclock. Referring to the example of FIG. 1, the third input 5 may receivea value of μ_(O,1) (i.e. ⅔ in units of the high frequency clock) inconnection with the first time interval, a value of μ_(O,2) inconnection with the second time interval and a value of one inconnection with the third time interval.

The second stage 2 includes a first output 6 configured to output datafiltered by the digital filter 200. For example, the output data may berepresented by a bit sequence clocked with the high frequency clock.Since the input data received at the first input 3 indicates a lowerfrequency clock than data provided by the first output 6, the digitalfilter 200 may be referred to as an interpolation filter. More detailedembodiments of interpolation filters corresponding to the digital filter200 will be described later.

FIG. 3 schematically illustrates a digital filter 300 as an exemplaryembodiment. The digital filter 300 includes a first stage 7 operating ata high frequency clock and a second stage 8 operating at a low frequencyclock, wherein a ratio μ_(I) of the low frequency clock and the highfrequency clock may correspond to a fractional number (cf. FIG. 1).

The first stage 7 includes a first input 9 configured to receive inputdata to be filtered by the digital filter 300. For example, the inputdata may be represented by a binary bit sequence clocked with the highfrequency clock. A second input 4 of the second stage 8 receives asignal representing the ratio μ_(I) of the low frequency clock and thehigh frequency clock, and a third input 5 receives a signal representinga time offset μ_(O) between a clock pulse of the high frequency clockand a clock pulse of the low frequency clock. Referring back to theexample of FIG. 1, the third input 5 may receive a value of μ_(O,1) inconnection with the first time interval, a value of μ_(O,2) inconnection with the second time interval and a value of one inconnection with the third time interval.

The second stage 8 further includes a first output 10 configured tooutput data filtered by the digital filter 300. For example, the outputdata may be represented by a binary bit sequence clocked with the lowfrequency clock. For the case of the digital filter 300, the input datareceived at the first input 9 has a higher frequency clock than thefiltered output data provided by the first output 10. The digital filter300 may thus be referred to as a decimation filter. More detailedembodiments of decimation filters corresponding to the digital filter300 will be described later.

FIG. 4 illustrates a pulse response 400 of a linear digital filter, i.e.a digital filter of order one. A pulse response describes the reactionof a digital filter on an input signal in form of a Dirac pulse. Thatis, the output signal of a digital filter may be determined by aconvolution of the pulse response with the corresponding input signal.In FIG. 4, the amplitude of the pulse response (cf. vertical axis) isplotted against time (cf. horizontal axis).

The pulse response 400 may be divided into a first time interval betweenthe times t₀ and t₁ and a second time interval between the times t₁ andt₂ with both time intervals having identical lengths. Each time intervalmay be divided in an arbitrary number of equidistant support points,wherein the length of the sub-time intervals in between these supportpoints may depend on a frequency of a clock. For example, the first timeinterval between the times t₀ and t₁ may correspond to the first timeinterval between the times t₀ and t_(1,1) of FIG. 1 and the second timeinterval between the times t₁ and t₂ may correspond to the second timeinterval between the times t_(1,1) and t_(1,2) of FIG. 1.

Each time interval of the pulse response 400 may be described by apolynomial P of order one, i.e. a straight line determined by twocoefficients of a linear equation. Since the pulse response 400 may bedivided into two straight lines (cf. first and second time interval inFIG. 4), the pulse response of the corresponding digital filter isdetermined by four filter coefficients k₁₁, k₁₂, k₂₁, k₂₂. These filtercoefficients may be written in form of a (2×2)-matrix such as

$\begin{matrix}{M = {\begin{pmatrix}k_{12} & k_{11} \\k_{22} & k_{21}\end{pmatrix}.}} & (1)\end{matrix}$

FIG. 5 schematically illustrates a digital interpolation filter 500 asan exemplary embodiment. The digital filter 500 represents a moredetailed implementation of the digital filter 200 and may be describedby the pulse response illustrated in FIG. 4.

The digital filter 500 includes a first stage 1 operating at a lowfrequency clock and a second stage 2 operating at a high frequencyclock, wherein a ratio μ_(I) of the frequency clocks may be fractionalnumber. The first stage 1 includes a first register 11, multipliers12.11, 12.12, 12.21, 12.22, calculation units 13.11, 13.12, 13.21, 13.22and adders 14.1, 14.2. The components of the first stage 1 are connectedwith each other via signal paths as illustrated in FIG. 5.

The digital filter 500 receives input data to be filtered (cf. “Input”),the ratio μ_(I) of the low frequency clock and the high frequency clockand the time offset μ_(O). These input values may be received by anarbitrary number of inputs of the digital filter 500. Each of thecalculation units 13.11 to 13.22 is configured to receive the valuesμ_(I) and μ_(O) and thus the input of the digital filter 500 receivingthe values of μ_(I) and μ_(O) is connected to the calculations units13.11 to 13.22.

The second stage 2 includes a closed-loop time-delay element having anadder 15 and a second register 16 arranged in series, wherein an outputof the second register 16 is connected to an input of the adder 15 via afeedback loop 17. The second stage 2 may be referred to as integratorstage and further includes an output (cf. “Output”) to provide datafiltered by the digital filter 500. The first stage 1 and the secondstage 2 are connected via sampling circuits 18.1 and 18.2.

The digital filter 500 further includes a counter configured to countdown an arbitrary number. For example, the counter may count down anumber of clock pulses of the high frequency clock occurring betweensucceeding clock pulses of the low frequency clock (cf. FIG. 1). Thecounter may be connected to the sampling circuit 18.2 in such a way thatthe sampling circuit 18.2 may set the second register 16 to apredetermined value when the counter has counted down the first number.The predetermined value may correspond to a value stored in the samplingcircuit 18.2.

In the following, an operating mode of the digital filter 500 will beexplained. The digital filter 500 receives input data of a low frequencyclock and processes the input data in various signal paths asillustrated in FIG. 5. Each of the calculation units 13.11 to 13.22calculates a different one of the filter coefficients k₁₁, k₁₂, k₂₁, k₂₂of the digital filter 500 which are then multiplied with the input databy means of the multipliers 12.11 to 12.22. Note that the matrix M ofequation (1) including the filter coefficients is arranged similar tothe calculation units 13.11 to 13.22 of FIG. 5. That is, the filtercoefficient k₁₁ is calculated by the calculation unit 13.11, the filtercoefficient k₁₂ is calculated by the calculation unit 13.12, etc. Ofcourse, the calculation units 13.11 to 13.22 may be combined in a singlecalculation unit. Note that input data passing the first register 11 isdelayed in comparison to input data not passing the first register 11.

The filter coefficients k₁₁, k₁₂, k₂₁, k₂₂ may depend on at least one ofthe ratio μ_(I) of the low frequency clock and the high frequency clockand the time offset μ_(O). The calculation of the filter coefficientsvia the calculation units 13.11 to 13.22 may be based on any functionalrelationship. The operating mode of the digital filter 500 may thus bedetermined by the specific configuration of the calculation units 13.11to 13.22.

The input data processed by the components (multipliers, adders, etc.)of the first stage 1 is forwarded to the sampling circuits 18.1 and 18.2via two signal paths. The sampling circuit 18.1 is clocked with the highfrequency clock and due to the summation performed by the adder 15, thevalue of the second register 16 is incremented at each clock pulse ofthe high frequency clock (cf. low peaks in FIG. 1). The sampling circuit18.2 sets the value of the second register 16 to a predetermined valueat each clock pulse of the high frequency clock following a clock pulseof the low frequency clock (cf. low peaks following the high peaks inFIG. 1). The times of these clock pulses are determined by the values ofthe time offset μ_(O) and the number of clock pulses of the highfrequency clock occurring between clock pulses of the low frequencyclock. In particular, at or otherwise responsive to the clock pulses ofthe high frequency clock, the sampling circuit 18.2 writes processedinput data received by the adder 14.2 into the second register 16.

For example, referring to the second time interval of FIG. 1, thecounter of the digital filter 500 counts down from a value of five (cf.the five low peaks occurring between the times t_(1,1) and t_(1,2)).Reaching the value of zero and taking into account the value of the timeoffset μ_(O,2), the sampling circuit 18.2 writes a predetermined valueinto the second register 16 at the time of, or otherwise responsive to,the clock pulse of the high frequency clock following the clock pulse ofthe low frequency clock at the time t_(1,2).

The matrix M including the filter coefficients k₁₁, k₁₂, k₂₁, k₂₂ of thedigital filter 500 may be derived to read

$\begin{matrix}{M = {\begin{pmatrix}1 & \mu_{O} \\{- 1} & {\frac{1}{\mu_{I}} - \mu_{O}}\end{pmatrix}.}} & (2)\end{matrix}$

FIG. 6 schematically illustrates a digital interpolation filter 600 asan exemplary embodiment. The digital filter 600 represents a moredetailed implementation of the digital filter 200. Similar to thedigital filter 500, the digital filter 600 may be described by the pulseresponse as illustrated in FIG. 4.

The digital filter 600 includes a first stage 1 operating at a lowfrequency clock and a second stage 2 operating at a high frequencyclock, wherein a ratio μ_(I) of the frequency clocks may be a fractionalnumber. The first stage 1 includes a first register 11, multipliers12.1, 12.2 and adders 14.1, 14.2. The components of the first stage 1are connected with each other via signal paths as illustrated in FIG. 6.

The first stage 1 includes an arbitrary number of inputs to receive datato be filtered (cf. “Input”), the ratio μ_(I) and the time offset μ_(O).It is understood that the input of the digital filter 600 is connectedto the multipliers 12.1 and 12.2 in such a way that the multipliers 12.1and 12.2 receive the parameters μ_(I) and μ_(O).

The second stage 2 of the digital filter 600 corresponds to the secondstage 2 of the digital filter 500. The same holds true for the couplingbetween the stages 1 and 2 via sampling circuits 18.1 and 18.2.Moreover, the digital filter 600 includes a counter as it has alreadybeen described in connection with FIG. 5.

In the following, differences between the first stages 1 of the digitalfilters 500 and 600 are considered. Both filters 500 and 600 are oforder one and are thus determined by four filter coefficients k₁₁, k₁₂,k₂₁, k₂₂. While the first stage 1 of the digital filter 500 includes amultiplier for each filter coefficient, the first stage 1 of the digitalfilter 600 merely includes two multipliers. This reduction ofmultipliers may lead to a reduction of computational steps and thus areduction of power consumption.

In contrast to the digital filter 500, the digital filter 600 does notinclude calculation units for calculating filter coefficients. In FIG.6, the input data is directly multiplied by the ratio μ_(I) and the timeoffset μ_(O) via the multipliers 12.1 and 12.2. Additional calculationsteps as they are performed by the calculation units 13.11 to 13.22 ofFIG. 5 are omitted. Generally, the multipliers 12.1 and 12.2 of thedigital filter 600 may receive and apply arbitrary values depending onthe ratio μ_(I) and the time offset μ_(O) according to any desiredfunctional relationship.

From FIGS. 5 and 6 it becomes apparent that the first stages 1 of thedigital filters 500 and 600 differ concerning their arrangements ofmultipliers and adders. As can be seen from FIG. 5, the first register11 of the digital filter 500 is coupled to the multipliers 12.11 to12.22, while the first register 11 of the digital filter 600 is coupledto the adders 14.1 and 14.2. Note that the first and second stages ofboth filters 500 and 600 include the same number of registers.

The matrix M including the filter coefficients of the digital filter 600may be derived to read

$\begin{matrix}{M = {\begin{pmatrix}\mu_{I} & {\mu_{O} \cdot \mu_{I}} \\{- \mu_{I}} & {1 - {\mu_{O} \cdot \mu_{I}}}\end{pmatrix}.}} & (3)\end{matrix}$

A comparison of equations (2) and (3) shows that the matrices M of thedigital filters 500 and 600 differ by a factor of μ_(I). This differenceresults in different filter gains.

FIG. 7 shows a pulse response 700 of a quadratic digital filter, i.e. adigital filter of order two. Similar to FIG. 4, the amplitude of thepulse response is plotted against time. The pulse response 700 may bedivided into a first time interval between the times t₀ and t₁, a secondtime interval between the times t₁ and t₂ and a third time intervalbetween the times t₂ and t₃.

The three time intervals of FIG. 7 may be identified with, for example,the three time intervals of the timing diagram 100. Similar to FIG. 4,the time intervals may be divided in an arbitrary number of equidistantsupport points or sub-time intervals in between these support points.

Each time interval of the pulse response 700 may be described by apolynomial P of order two, i.e. a quadratic function determined by threecoefficients. Since the pulse response 700 may thus be represented bythree quadratic functions with the pulse response of the correspondingdigital filter being determined by nine filter coefficients k₁₁, k₁₂,k₁₃, k₂₁, k₂₂, k₂₃, k₃₁, k₃₂, k₃₃. These filter coefficients may bewritten in form of a (3×3)-matrix such as

$\begin{matrix}{M = {\begin{pmatrix}k_{13} & k_{12} & k_{11} \\k_{23} & k_{22} & k_{21} \\k_{33} & k_{32} & k_{31}\end{pmatrix}.}} & (4)\end{matrix}$

FIG. 8 schematically illustrates a digital interpolation filter 800 asan exemplary embodiment. For the sake of simplicity, not all componentsof the digital filter 800 are labeled by reference signs. The digitalfilter 800 represents a more detailed implementation of the digitalfilter 200 and may be described by the pulse response as illustrated inFIG. 7.

The digital filter 800 shows a design similar to the digital filter 500.Since the pulse response of the digital filter 800 depends on ninefilter coefficients, the number of multipliers, adders and calculationunits of the first stage 1 is extended to a quantity of nine. Moreover,the first stage 1 and the second stage 2 each includes two registers11.1, 11.2, 16.1 and 16.2, respectively. Since there are three signalpaths coupling the first stage 1 and the second stage 2, the digitalfilter 800 includes three sampling circuits 18.1, 18.2 and 18.3.

The operating mode of the digital filter 800 corresponds to theoperating mode of the digital filter 500 and becomes apparent from thedescription of FIG. 5. FIGS. 5 and 8 further show that similar filtersof order n>2 may be designed in a straightforward way by simply addingcolumns and rows of multipliers, adders, etc.

One example of a digital filter 800 of order two is a digital filterperforming a quadratic Lagrange interpolation. The associated matrix Mof filter coefficients may be derived to read

$\begin{matrix}{M = {\begin{pmatrix}2 & {1 + {2\mu_{O}}} & {{- \frac{1}{4\mu_{I}^{2}}} + \mu_{O}^{2}} \\{- 4} & {{- 2} + \frac{2}{\mu_{I}} - {4\mu_{O}}} & {\frac{3}{2\mu_{I}^{2}} + \frac{2\mu_{O}}{\mu_{I}} - {2\mu_{O}^{2}}} \\2 & {1 - \frac{2}{\mu_{I}} + {2\mu_{O}}} & {\frac{3}{4\mu_{I}^{2}} - \frac{2\mu_{O}}{\mu_{I}} + \mu_{O}^{2}}\end{pmatrix}.}} & (5)\end{matrix}$

Here, the filter gain depends on the interpolation factor. By dividingthe matrix M by a factor of

$\frac{2}{\mu_{I}^{2}},$the filter gain may be scaled to a constant value of one.

An example for a digital filter 800 of order two is a digital filterperforming a quadratic B-Spline interpolation. The associated matrix Mof filter coefficients may be derived to read

$\begin{matrix}{M = {\begin{pmatrix}2 & {1 + {2\mu_{O}}} & \mu_{O}^{2} \\{- 4} & {{- 2} + \frac{2}{\mu_{I}} - {4\mu_{O}}} & {\frac{1}{\mu_{I}^{2}} + \frac{2\mu_{O}}{\mu_{I}} - {2\mu_{O}^{2}}} \\2 & {1 - \frac{2}{\mu_{I}} + {2\mu_{O}}} & {\frac{1}{\mu_{I}^{2}} - \frac{2\mu_{O}}{\mu_{I}} + \mu_{O}^{2}}\end{pmatrix}.}} & (6)\end{matrix}$

Again, the filter gain depends on the interpolation factor. Dividing thematrix M by a factor of

$\frac{2}{\mu_{I}^{2}}$leads to a filter gain of a constant value of one.

FIG. 9 schematically illustrates a digital interpolation filter 900 asan exemplary embodiment. The digital filter 900 represents a moredetailed implementation of the digital filter 200 and performs aquadratic Lagrange interpolation. For the sake of simplicity, not allcomponents of the digital filter 900 are labeled by reference signs.

The first stage 1 of the digital filter 900 includes two first registers11.1, 11.2, multiple adders and multiple multipliers. The multipliers12.1 and 12.2 multiply the input data with a value of μ_(O), themultiplier 12.3 multiplies the input data with a value of 1/μ_(I) andthe multiplier 12.4 multiplies the input data with a value of 1/μ_(I) ².The digital filter 900 may directly receive the required values 1/μ_(I)and 1/μ_(I) ² or may alternatively include additional calculation unitsto calculate these values from an input value of μ_(I).

The digital filter 900 includes further units performing multiplicationoperations of input data. In FIG. 9, these multiplication operations aredenoted by numerical values such as a value of “−2” shown over thesignal path between the adder 14.1 and the node 19.1 or a value of “½”shown over the signal path between the adder 14.2 and the node 19.2. Forexample, the value of “−2” denotes a multiplication by a value of minustwo, while the value “½” denotes a multiplication by a value of one halfwhich may be performed by shifting bits representing the input data.

The digital filters 800 and 900 mainly differ concerning the samefeatures as the digital filters 500 and 600 which have been describedabove. For example, the digital filter 900 includes fewer adders andfewer multipliers than the digital filter 800 and thus may exhibit areduced power consumption.

The matrix M including the filter coefficients of the digital filter 900may be derived to read

$\begin{matrix}{M = {\begin{pmatrix}1 & {\frac{1}{2} + \mu_{O}} & {{- \frac{1}{8\mu_{I}^{2}}} + \frac{\mu_{O}^{2}}{2}} \\{- 2} & {{- 1} + \frac{1}{\mu_{I}} - {2\mu_{O}}} & {\frac{3}{4\mu_{I}^{2}} + \frac{\mu_{O}}{\mu_{I}} - \mu_{O}^{2}} \\1 & {\frac{1}{2} - \frac{1}{\mu_{I}} + \mu_{O}} & {\frac{3}{8\mu_{I}^{2}} - \frac{\mu_{O}}{\mu_{I}} + \frac{\mu_{O}^{2}}{2}}\end{pmatrix}.}} & (7)\end{matrix}$

A comparison of equations (5) and (7) shows that the matrices M of thedigital filters 800 and 900 differ by a factor of two. Note that, exceptfor a factor of two, both digital filters 800 and 900 show identicalpulse responses. For the case of equation (7) the filter gain depends onthe interpolation factor.

FIG. 10 schematically illustrates a digital interpolation filter 1000 asan exemplary embodiment. For the sake of simplicity, not all componentsare labeled by reference signs. Similar to the digital filter 900, thedigital filter 1000 performs a quadratic Lagrange interpolation. Thedigital filters 900 and 1000 differ in the arrangement of themultipliers 12.3 and 12.4, as well as the input values of thesemultipliers. While the multipliers 12.3 and 12.4 of the digital filter900 receive values of 1/μ_(I) and 1/μ_(I) ², the multipliers 12.3 and12.4 of the digital filter 1000 receive input values of μ_(I) and μ_(I)².

The matrix M including the filter coefficients of the digital filter1000 may be derived to read

$\begin{matrix}{M = {\begin{pmatrix}\mu_{I}^{2} & {\frac{\mu_{I}^{2}}{2} + {\mu_{O}\mu_{I}^{2}}} & {{- \frac{1}{8}} + \frac{\mu_{O}^{2}\mu_{I}^{2}}{2}} \\{{- 2}\mu_{I}^{2}} & {{- \mu_{I}^{2}} + \mu_{I} - {2\mu_{O}\mu_{I}^{2}}} & {\frac{3}{4} + {\mu_{O}\mu_{I}} - {\mu_{O}^{2}\mu_{I}^{2}}} \\\mu_{I}^{2} & {\frac{\mu_{I}^{2}}{2} - \mu_{I} + {\mu_{O}\mu_{I}^{2}}} & {\frac{3}{8} - {\mu_{O}\mu_{I}} + \frac{\mu_{O}^{2}\mu_{I}^{2}}{2}}\end{pmatrix}.}} & (8)\end{matrix}$

A comparison of equations (7) and (8) shows that the matrices M of thedigital filters 900 and 1000 differ by a factor of μ_(I) ². The filtergain of the digital filter 1000 is one.

FIG. 11 schematically illustrates a digital decimation filter 1100 as anexemplary embodiment. The digital filter 1100 represents a more detailedimplementation of the digital filter 300 and may be described by thepulse response illustrated in FIG. 4. The digital decimation filter 1100may be seen as a counterpart of the digital interpolation filter 500.

The digital filter 1100 includes a first stage 7 operating at a highfrequency clock and a second stage 8 operating at a low frequency clock,wherein a ratio μ_(I) of the frequency clocks may be a fractionalnumber. The first stage 7 includes two closed-loop time-delay elementshaving an adder 15.1 (15.2) and a first register 16.1 (16.2),respectively. An output of each first register 16.1 (16.2) is connectedto an input of the adder 15.1 (15.2) via a feedback loop 17.1 (17.2).The first stage 7 may be referred to as integrator stage and includes afirst input (cf. “Input”) to receive data to be filtered. Note that thefirst stage 7 of the digital filter 1110 includes an additionalclosed-loop time-delay element compared to the second stage 2 of thedigital filter 500.

The second stage 8 includes a first register 11, multipliers 12.11,12.12, 12.21, 12.22, calculation units 13.11, 13.12, 13.21, 13.22 andadders 14.1, 14.2, 14.3. The components of the second stage 8 areconnected with each other via signal paths as illustrated in FIG. 11.Note that the digital filter 1100 may be extended to a filter of ordern>1 in a straightforward way by adding further columns and rows ofmultipliers, adders, etc.

The second stage 8 includes an arbitrary number of inputs to receive theratio μ_(I) and the time offset μ_(O). Each calculation unit 13.11 to13.22 is configured to receive the values μ_(I) and μ_(O) and thus theinput of the digital filter 1100 is connected to the calculations units13.11 to 13.22. The second stage 8 further includes an output (cf.“Output”) to provide filtered output data. The first stage 7 and thesecond stage 8 are connected by sampling circuits 18.1 and 18.2.

Similar to the digital filter 500, the digital filter 1100 includes acounter (not illustrated) to count down arbitrary numbers. For example,the counter may count down a number of clock pulses of the highfrequency clock occurring between succeeding clock pulses of the lowfrequency clock (cf. FIG. 1). The counter is connected to the registers16.1 and 16.2 (cf. “Reset”) in such a way that these registers may beset to a predetermined value (preferably a value of zero) when thecounter has count down.

The operating mode of the digital filter 1100 becomes apparent from thedescription of the operating mode of the digital filter 500. Bothfilters 500 and 1100 process data to be filtered in a similar way, butin opposite directions. For the case of the digital filter 500, inputdata is interpolated by converting it from a low frequency clock to ahigh frequency clock, while the digital filter 1100 decimates input datato be filtered by converting it from a high frequency clock to a lowfrequency clock. Note that the registers 16.1 and 16.2 are preferablyreset to a predetermined value at a clock pulse of the high frequencyclock following a clock pulse of the low frequency clock. Before theregisters 16.1 and 16.2 are reset, the sampling circuits 18.1 and 18.2read out the values stored in the registers 16.1 and 16.2 and forwardthese values to the second stage 8.

The filter coefficients of the digital filter 1100 may be expressedaccording to equation (1). Similar to FIG. 5, the calculation units13.11 to 13.22 of FIG. 11 are arranged according to the filtercoefficients of the matrix M in equation (1). That is, the filtercoefficient k₁₁ is calculated by the calculation unit 13.11, the filtercoefficient k₁₂ is calculated by the calculation unit 13.12, etc. Acomparison of FIGS. 5 and 11 shows that the designs of the digitalfilters 500 and 1100 are mirror-inverted to each other with respect to avertical axis. For example, the register 11 in FIG. 5 is arranged on thevery left, while the register 11 in FIG. 11 is arranged on the veryright. Moreover, the calculation unit 13.12 in FIG. 5 corresponds to thecalculation unit 13.11 in FIG. 11, the calculation unit 13.22 in FIG. 5corresponds to the calculation unit 13.21 in FIG. 11, etc. Themirror-inversion corresponds to an exchange of columns in the matrix Mof filter coefficients.

If a decimator structure would emerge from the interpolator structure ofFIG. 5 by purely inverting the direction of the data to be filtered,this data would pass the register 11 of the resulting decimator in adirection (bottom-up) which is opposite to the direction of the datapassing the register 11 of the integrator 500 (top down). However, inFIG. 11 the data to be filtered passes the register 11 similar to FIG. 5(top down). This results in an exchange of the rows in the matrix M offilter coefficients. In summary, the matrix M of filter coefficients forthe digital filter 1100 may thus be obtained from the matrix M of filtercoefficients for the digital filter 500 (cf. equation (2)) by exchangingcolumns and rows, as follows:

$\begin{matrix}{M = {\begin{pmatrix}{\frac{1}{\mu_{I}} - \mu_{O}} & {- 1} \\\mu_{O} & 1\end{pmatrix}.}} & (9)\end{matrix}$

FIG. 12 schematically illustrates a digital decimation filter 1200 as anexemplary embodiment, wherein not all components are labeled byreference signs. The digital filter 1200 represents a more detailedimplementation of the digital filter 300 and may be described by a pulseresponse illustrated in FIG. 4.

The digital filter 1200 includes a first stage 7 operating at a highfrequency clock and a second stage 8 operating at a low frequency clock,wherein a ratio μ_(I) of the frequency clocks may be a fractionalnumber. The first stage 7 of the digital filter 1200 corresponds to thefirst stage 7 of the digital filter 1100. The same holds true for thecoupling between the stages 7 and 8 via sampling circuits 18.1 and 18.2.The second stage 8 includes a register 11, multipliers 12.1, 12.2,adders 14.1, 14.2 and an adding unit 20. The components of the secondstage 8 are connected with each other via signal paths as it isillustrated in FIG. 12.

Again, the digital filter 1200 includes a counter to count down anarbitrary number as it has already been described in connection withprevious figures. The registers 16.1 and 16.2 of the first stage 7 maybe set to an arbitrary value via a signal line 21.

The first stage 7 receives data to be filtered (cf. “Input”), while thesecond stage 8 provides filtered output data (cf. “Output”). Theoperating mode of the digital filter 1200 becomes apparent from thedescription of previous embodiments. The matrix M including the filtercoefficients of the digital filter 1200 may be derived to read

$\begin{matrix}{M = {\begin{pmatrix}{1 - {\mu_{O} \cdot \mu_{I}}} & {- \mu_{I}} \\{\mu_{O} \cdot \mu_{I}} & \mu_{I}\end{pmatrix}.}} & (10)\end{matrix}$

A comparison of equations (9) and (10) shows that the matrices M of thedigital filters 1100 and 1200 differ by a factor of μ_(I). Thisdifference results in different filter gains.

From the timing diagram 100 of FIG. 1 it becomes apparent that thenumber of clock pulses of the high frequency clock occurring betweenclock pulses of the low frequency clock may vary. Here, the timingdiagram 100 showed possible values of five and six. Pulse responses ofdigital filters as illustrated in FIGS. 4 and 7 may thus differ in theirrespective lengths. The decimation filters 1100 and 1200 are configuredto filter input data, wherein the length of the employed pulse responsemay vary over time. It may, however, be desirable to employ pulseresponses of a fixed length. A digital filter 1300 supporting afiltering based on pulse responses of fixed length will be described inthe following.

FIG. 13 schematically illustrates a digital decimation filter 1300 as anexemplary embodiment. For the sake of simplicity, not all components ofthe filter 1300 are labeled by reference signs. The digital filter 1300may be described by a pulse response of a fixed length as illustrated inFIG. 4.

The digital filter 1300 includes a first stage 7 operating at a highfrequency clock and a second stage 8 operating at a low frequency clock,wherein a ratio μ_(I) of the frequency clocks may be fractional number.The first stage 7 includes an input (cf. “Input”) to receive data to befiltered. The input of the first stage 7 is connected to a first (upper)and a second (lower) signal path, wherein each of these signal pathscorresponds to the signal path in the first stage 7 of the digitalfilter 1200.

The first stage 7 and the second stage 8 are connected via pairs ofsampling circuits 18.1, 18.2 and a sampling circuit 18.3. Each of thepairs includes a sampling circuit connected with the output of aregister of the first signal path as well as a sampling circuitconnected with a register of the second signal path. Detailedconnections become apparent from FIG. 13.

Similar to the digital filter 1100, the second stage 8 of the digitalfilter 1300 includes multiple multipliers, calculation units and adders,the arrangement of which can be seen from FIG. 13. In addition, thesecond stage 8 includes an addition unit 20, two pairs of registers 22.1and 22.2 and switches 23.11 to 23.22 to switch between signal lines asillustrated in FIG. 13. Note that the digital filter 1300 may beextended to a digital filter of order n>1 in a straightforward way byadding additional columns and rows including multiplication units,adders, multipliers, etc.

Again, the digital filter 1300 includes a counter to count down anarbitrary number. The counter may be included, for example, in a controlunit 24 to control the time when the switches 23.11 to 23.22 switchbetween signal lines as illustrated in FIG. 13. Further, the controlunit 24 controls the time when the registers 16.1, 16.2, 16.1′ and 16.2′of the first stage 7 are set to a predetermined value. The control unit24 is connected to a reset unit 25 which generates the reset of thefirst registers 16.1 to 16.2′.

The operating mode of the digital filter 1300 partly corresponds to theoperating mode of the digital filter 1100. For example, the calculationunits 13.11 to 13.22 operate in a similar way. A difference between theoperating modes of the digital filters 1100 and 1300 results fromadditional components included in the digital filter 1300, in particularfrom the second signal path in the first stage 7 and the additionalswitches 23.11 to 23.22 in the second stage 8.

FIG. 14 schematically illustrates a diagram 1400 illustrating anoperating mode of the digital filter 1300. Here, the ratio of the lowfrequency clock and the high frequency clock has a value 16/3. Thediagram 1400 includes a first part A illustrating an example of a timingdiagram, a second part B relating to an example of the operation of theupper signal path of the first stage 7 and a third part C relating to anexample of the operation of the lower signal path of the first stage 7.In the following, the upper and lower signal path of the first stage 7may also be denoted as first and second integrator paths, respectively.

Part A of the diagram 1400 shows arrows representing clock pulses of thehigh frequency clock. The arrows indicate time intervals lying inbetween, wherein numbers located between the arrows indicate the lengthsof the time intervals in units of the cycle duration of the highfrequency clock. For example, the time intervals labeled by “5” have alength of five cycle durations of the high frequency clock. Note thatthe time intervals indicated by “5” include further clock pulses of thehigh frequency clock which are not explicitly illustrated for the sakeof simplicity.

Part B of the diagram illustrates an operating mode of the firstintegrator path of the digital filter 1300. Here, a first operatingperiod is illustrated by a first block B.1. A first integrationperformed by the first integrator path and associated with an offsetvalue μ_(O) of zero is indicated by two rectangles (cf. “Oldintegration” and “New integration”). The first integration starts at atime t₁ and ends at a time t₁₁ and thus has a length of ten cycledurations of the high frequency clock.

The integration indicated by said two rectangles corresponds to anintegration over one pulse response. Note that FIG. 14 relates to alinear filter having a pulse response similar to FIG. 4. The firstrectangle (cf. “Old integration”) indicates an integration over theascending part of the pulse response 400, while the second rectangle(cf. “New integration”) indicates an integration over the descendingpart of the pulse response 400. The pulse response thus has a length often cycle durations of the high frequency clock. Of course, during anoperation of the first integrator path, the switches 23.11 to 23.22 ofthe digital filter 1300 are in a position connecting the firstintegrator path to the second stage 8.

Still referring to the first block B.1, a second integration associatedwith an offset value μ_(O) of ⅓ is similarly indicated by tworectangles. The second integration starts at a time t₆ and ends at thetime t₁₁. In block B.1, the new integration for an offset value μ_(O) ofzero overlaps with the old integration for an offset value μ_(O) of ⅓.This overlap does not indicate a twofold integration of the firstintegrator path, but is meant to indicate that these two integrationsare identical. The first block B.1 further shows a third integrationwhich has a length of five clock periods of the high frequency clock andstarts at the time t₁₁. The registers 16.1 and 16.2 of the firstintegrator path are reset to a predetermined value (preferably a valueof zero) at start times of the old integrations, i.e. at the times t₁,t₆, t₁₁ and t₁₆.

Part C of the diagram illustrates an operating mode of the secondintegrator path of the digital filter 1300. A block C.1 illustrates anoperating period including three integrations, each integration beingassociated with an offset value μ_(O). Concerning its structure, theblock C.1 corresponds to the block B.1. The times indicating the startand end points of the three integrations become apparent from FIG. 14.

Note that the start of the old integration associated with an offsetvalue μ_(O) of zero in block C.1 (cf. time t₁₇) is delayed or shifted byone clock duration of the high frequency clock with respect to the startof the new integration associated with an offset value μ_(O) of ⅔ inblock B.1 (cf. time t₁₆). At a time t₂₁, the integration associated withan offset value μ_(O) of ⅔ in block B.1 is finished, while, at a timet₂₇, the integration associated with an offset value μ_(O) of zero inblock C.1 is finished. The switches 23.11 to 23.22 of the digital filter1300 thus preferably switch their position at a time lying between atime t₂₂ and the time t₂₇, thereby connecting the second integrator pathof the first stage 7 to the second stage 8. Similar to the block B.1,the registers 16.1′ and 16.2′ of the second integrator path are reset toa predetermined value (preferably a value of zero) at the timesindicating a start of an old integration.

Part B includes a second block B.2 illustrating a further operatingperiod of the first integrator path. Again, the start of the oldintegration associated with an offset value μ_(O) of zero in block B.2is delayed or shifted by one clock duration of the high frequency clockwith respect to the start of the new integration associated with anoffset value μ_(O) of ⅔ in block C.1. Moreover, the registers 16.1 and16.2 of the first integrator path are reset to a predetermined value(preferably a value of zero) at the times at the start indicating astart of an old integration. At a time t₃₇, the integration associatedwith an offset value μ_(O) of ⅔ in block C.1 is finished, while, at atime t₄₃, the integration associated with an offset value μ_(O) of zeroin block B.2 is finished. The switches 23.11 to 23.22 of the digitalfilter 1300 thus preferably switch their position at a time lyingbetween a time t₃₈ and the time t₄₃, thereby connecting the firstintegrator path of the first stage 7 to the second stage 8.

The digital filters described above use the value of the time offsetμ_(O) and the number of clock pulses of the high frequency occurringbetween clock pulses of the low frequency clock. The followingdescription is dedicated to a digital device providing these values.

FIG. 15 schematically illustrates a digital device 1500 which may alsobe denoted by the reference sign 26. The device 26 includes a firstinput 27, a first output 28 and a second output 29, wherein the firstinput 27 is connected to a third adder 30. The third adder 30 isconnected to a first (upper) signal path, a second (middle) signal pathand a third (lower) signal path.

The first signal path includes a first adder 31, a first discarding unit32, a first register 33 and a NOT gate 34 arranged in series. The firstregister 33 and the first adder 31 are connected by a feedback loop 35.The output of the NOT gate 34 is connected to the second output 29. Thesecond signal path includes a second discarding unit 36 and a comparisonunit 37 arranged in series. The comparison unit 37 is connected to thefirst signal path at a contact arranged between the first discardingunit 32 and the first register 33. The third signal path includes athird discarding unit 38, a second adder 39 and a switch 40. The switch40 includes two switch positions selectively connecting the first output28 to the third discarding unit 38 or the second adder 39. Moreover, theswitch 40 is connected to the comparison unit 37 and a second register42. The device 26 further includes a second input 41 connected to thethird adder 30.

In the following, an operating mode of the device 1500 will be explainedusing the timing diagram 100 of FIG. 1. The first time interval betweenthe times t₀ and t_(1,1) corresponds to a first operation cycle of thedevice 1500. A ratio of a low frequency clock and a high frequency clockis input into the first input 27 of the device 1500. A data wordrepresenting this ratio may, for example, be represented by 29 (e.g.,unsigned) bits, wherein the 6 most significant bits (MSB) represent aninteger portion of the ratio and the remaining 23 least significant bits(LSB) represent a decimal portion of the ratio. For the case of thetiming diagram 100, the ratio might have a value of 16/3. Accordingly,the six MSB represent an integer portion of five and the 23 LSBrepresent a decimal portion of ⅓.

The ratio of the low frequency clock and the high frequency clock may becorrected by a correction value provided by the second input 41. Thecorrection value is added to the ratio via the third adder 30. Such acorrection may be helpful for the case of unstable frequency clocks thatmay occur for the case of unstable oscillators generating the frequencyclocks. In the following example, the correction value is assumed to bezero.

The fractional value of 16/3 is forwarded to the first adder 31. Sincethe first register 33 is set to a value of zero for the first operationcycle of the device 1500, the feedback loop 35 provides a value of zeroto the first adder 31. The first discarding unit 32 thus receives avalue of 16/3 and discards, e.g., deletes, the six MSB representing theinteger portion of 16/3, i.e. a value of five. The remaining 23 LSBrepresenting a value of ⅓ are forwarded to the first register 33. TheNOT gate 34 receives the value of ⅓ and subtracts this value from avalue of one leading to a value of ⅔ forwarded to the second output 29.The described subtraction corresponds to inverting the 23 LSB and maythus also be referred to as an inversion.

Still referring to the first operation cycle of the device 1500, thesecond discarding unit 36 in the second signal path discards the six MSBand forwards the remaining 23 LSB representing a value of ⅓ to thecomparison unit 37. In the lower signal path, the third discarding unit38 discards the 23 LSB (i.e. a decimal portion of ⅓) and outputs theremaining six MSB representing a value of five. For the first operationcycle, the switch 40 is set to a default first switch positionconnecting the first output 28 to the output of the third discardingunit 38.

The comparison unit 37 compares a value x received from the firstdiscarding unit 32 and a value y received from the second discardingunit 36. If the value x is smaller than the value y, then in responsethe comparison unit 37 controls the switch 40 in such a way that theswitch 40 changes from the first switch position to a second switchposition connecting the first output 28 to the second adder 39. If theswitch 40 is in the second switch position, then in response the secondadder 39 adds a value of one to the value output by the third discardingunit 38. In the first operation cycle, the values x and y both equal ⅓and thus the switch 40 does not change from the first to the secondswitch position. Since no value of one is added by the second adder 39during the first operation cycle, the first output 28 outputs a value offive.

In accordance with the timing diagram 100, the second output 29 outputsa value of ⅔ corresponding to the time offset μ_(O,1) and the firstoutput 28 outputs a value of five corresponding to the number of clockpulses of the high frequency clock occurring during the first timeinterval between the times t₀ and t_(1,1).

In the following, the second and third operation cycle of the device1500 will be explained. Here, the second operation cycle corresponds tothe second time interval between the times t_(1,1) and t_(1,2) and thethird operation cycle corresponds to the third time interval between thetimes t_(1,2) and t_(1,3). For a better understanding, the followingTable 1 shows illustrative values at different locations in the device1500 during its different operation cycles.

TABLE 1 Cycle No. a b c μ_(O) n 1 16/3 1/3 5 2/3 5 2 16/3 2/3 5 1/3 5 316/3 0 5 1 6

In Table 1, the parameter a denotes the value input to the first input27, the parameter b denotes the value output by the first discardingunit 32, the parameter c denotes the value output by the thirddiscarding unit 38, the value μ_(O) denotes the time offset output bythe second output 29 and the parameter n denotes the number of highfrequency clock pulses occurring during the regarded time intervaloutput by the first output 28.

For the first operation cycle, the table values have already beenderived: a= 16/3, b=⅓, c=5, μ_(O)=⅔ and n=5. Referring now to the secondoperation cycle, the ratio of the low frequency clock and the highfrequency clock remains the same, i.e. a= 16/3. The first adder 31 addsa value of 16/3 and a value of ⅓ (provided by the feedback loop 35)leading to a value of 17/3, the integer portion of which is discarded bythe first discarding unit 32. Therefore, b equals a value of ⅔. Notethat the addition performed by the first adder 31 may lead to anadditional MSB for proper representation of the integer portion of theratio. An inversion performed by the NOT gate 34 leads to a time offsetvalue μ_(O) of ⅓ for the second operation cycle output by the secondoutput 29.

Due to discarding the decimal portion of the input ratio 16/3, the thirddiscarding unit 38 outputs a value c of five. Since x equals ⅔ and yequals ⅓, the switch 40 does not change to the second switch positionconnecting the first output 28 to the second adder 39. Accordingly, thesecond adder 39 does not add a value of one and the first output 28outputs a value of five.

Referring now to the third operation cycle, the ratio input at the firstinput 27 still remains the same, i.e. a= 16/3. The first adder 31 adds avalue of 16/3 and a value of ⅔ (provided by the feedback loop 34)leading to a value of 18/3, whose integer portion of six is discarded bythe first discarding unit 32. Therefore, b equals zero and the NOT gate34 forwards a time offset μ_(O) of one to the second output 29.

Due to discarding the decimal portion of the input ratio 16/3, the thirddiscarding unit 38 again outputs a value c of five. Since x now equalszero and y equals ⅓, the switch 40 changes from the first switchposition to the second switch position connecting the first output 28 tothe second adder 39. Accordingly, the second adder 39 adds a value ofone to the value c and the first output 28 outputs a value of six.

As already mentioned in the description of FIG. 1, later time intervalsmay be obtained by simply repeating the first three time intervals. Forexample, a fourth time interval would then correspond to the first timeinterval, a fifth time interval would correspond to the second timeinterval, etc. In this connection, it is to be noted that the firstregister 33 may be reset to a value of zero after the third timeinterval has passed.

What is claimed is:
 1. A digital filter, comprising: a first stageconfigured to operate with a first computational complexity and a firstfrequency clock; and a second stage configured to operate with a secondcomputational complexity and a second frequency clock, wherein: thedigital filter is configured to transmit at least two signals betweenthe first stage and the second stage, the second frequency clock is of agreater frequency than the first frequency clock, the firstcomputational complexity is greater than the second computationalcomplexity, and the ratio of the first frequency clock to the secondfrequency clock is fractional.
 2. The digital filter of claim 1,wherein: the first computational complexity is based on a number offirst computational operations performed by the first stage during afirst time interval; and the second computational complexity is based ona number of second computational operations performed by the secondstage during the first time interval.
 3. The digital filter of claim 1,wherein: the first computational complexity is based on a number offirst computational operations performed by the first stage during aclock cycle of the first frequency clock; and the second computationalcomplexity is based on a number of second computational operationsperformed by the second stage during a clock cycle of the firstfrequency clock.
 4. The digital filter of claim 1, wherein: the firstcomputational complexity is based on a number of first computationaloperations performed by the first stage, wherein the first computationaloperations comprise processing data based on filter coefficients of thedigital filter; and the second computational complexity is based on anumber of second computational operations performed by the second stage,wherein the second computational operations comprise integrating datareceived from the first stage.
 5. The digital filter of claim 1, whereina power consumption of the first stage during a clock cycle of the firstfrequency clock is greater than a power consumption of the second stageduring a clock cycle of the second frequency clock.
 6. The digitalfilter of claim 1, wherein the first stage and the second section arecoupled together by an interface unit.
 7. The digital filter of claim 6,wherein the interface unit comprises a sampling unit clocked with thesecond frequency clock.
 8. The digital filter of claim 1, wherein thefirst stage comprises an input configured to receive input data to befiltered and the second stage comprises an output configured to providefiltered output data.
 9. The digital filter of claim 1, wherein thesecond stage comprises an input configured to receive input data to befiltered and the first stage comprises an output configured to providefiltered output data.
 10. The digital filter of claim 1, wherein thedigital filter is of order n, a pulse response of the digital filter isdetermined by (n+1)² filter coefficients of the digital filter, andthere are (n+1)² multipliers in the first stage, each of the multipliersconfigured to multiply input data with a respective one of the filtercoefficients of the digital filter.
 11. The digital filter of claim 1,wherein the digital filter is of order n, a pulse response of thedigital filter is determined by (n+1)² filter coefficients of thedigital filter, and there are less than (n+1)² multipliers in the firststage.
 12. A method, comprising: operating a first stage of a digitalfilter with a first computational complexity and a first frequencyclock; operating a second stage of the digital filter with a secondcomputational complexity and a second frequency clock; and transmittingat least two signals between the first stage and the second stage,wherein: the second frequency clock is of a greater frequency than thefirst frequency clock, the first computational complexity is greaterthan the second computational complexity, and the ratio of the firstfrequency clock to the second frequency clock is fractional.
 13. Themethod of claim 12, further comprising: performing a number of firstcomputational operations by the first stage during a first timeinterval, wherein the first computational complexity is based on thenumber of first computational operations; and performing a number ofsecond computational operations by the second stage during the firsttime interval, wherein the second computational complexity is based onthe number of second computational operations.
 14. The method of claim12, further comprising: performing a number of first computationaloperations by the first stage during a clock cycle of the firstfrequency clock, wherein the first computational complexity is based onthe number of first computational operations; and performing a number ofsecond computational operations by the second stage during the clockcycle of the first frequency clock, wherein the second computationalcomplexity is based on the number of second computational operations.15. The method of claim 12, further comprising: performing a number offirst computational operations by the first stage, wherein the firstcomputational complexity is based on the number of first computationaloperations and the first computational operations comprise processingdata based on filter coefficients of the digital filter; and performinga number of second computational operations by the second stage, whereinthe second computational complexity is based on the number of secondcomputational operations and the second computational operationscomprise integrating data received from the first stage.
 16. The methodof claim 12, wherein a power consumption of the first stage during aclock cycle of the first frequency clock is greater than a powerconsumption of the second stage during a clock cycle of the secondfrequency clock.
 17. The method of claim 12, further comprising:receiving input data at an input of the first stage; filtering the inputdata to generate filtered output data; and providing the filtered outputdata at an output of the second stage.
 18. The method of claim 12,further comprising: receiving input data at an input of the secondstage; filtering the input data to generate filtered output data; andproviding the filtered output data at an output of the first stage. 19.A digital filter, comprising: a first stage configured to operate with afirst frequency clock; and a second stage configured to operate with asecond frequency clock, wherein: the digital filter is configured totransmit at least two signals between the first stage and the secondstage, the second frequency clock is of a greater frequency than thefirst frequency clock, a power consumption of the first stage during aclock cycle of the first frequency clock is greater than a powerconsumption of the second stage during a clock cycle of the secondfrequency clock, and the ratio of the first frequency clock to thesecond frequency clock is fractional.
 20. A method, comprising:operating a first stage of a digital filter with a first frequencyclock; operating a second stage of a digital filter with a secondfrequency clock; and transmitting at least two signals between the firststage and the second stage, wherein: the second frequency clock is of agreater frequency than the first frequency clock, a power consumption ofthe first stage during a clock cycle of the first frequency clock isgreater than a power consumption of the second stage during a clockcycle of the second frequency clock, and the ratio of the firstfrequency clock to the second frequency clock is fractional.